<p>Climate and weather related events such as flooding, wildfires and cyclones pose significant risks to society. The overall impact of these events is determined by the interaction of many processes acting together, where the manner in which the processes are combined is often just as important as the state (extreme or otherwise) of each of the driving variables. In this sense, almost all events can be thought of as compound events, governed by many interacting variables acting on multiple spatial and temporal scales. Understanding the compound nature of events becomes particularly important in the quest to better understand and estimate risks under a changing climate. This is because the non-stationary nature of many of the driving variables implies that an impact cannot be accurately understood without understanding both the changes in each of the relevant variables as well as their interactions, as there are many instances where the relevant variables are expected to change at different rates and sometimes even in opposing directions. We therefore argue for a greater emphasis by the climate research community on the analysis of dependence between variables to better define, detect and model all relevant occurrences of extremes that may lead to a significant impact. As difficult as the technical challenge may be, understanding the compound nature of extreme events is essential to fully understanding their impact in a future climate.</p>